Math 410 Homework, Fall 2020

There will be 15 collected homework assignments worth 10 points each. These are given below, but are subject to changes announced in class. Only your 10 best homework scores count toward your course grade.

How and When to Turn in Your Homework. Each Homework should be submitted as a pdf file through ELMS by 11:00am of the due date.

How Each Homework Should Look. Your homework should be neat and legible. You should give the number of each problem attempted and the work for each problem should be indicated clearly. (There should be no arrows running around or between pages!) The reasoning behind each answer should be given. Your answers should be presented in the order that the problems are assigned. If you use more than one sheet of paper, they should be stapled together. The top of the first page should include: your name, our course and section number, my name, and the date the assignment is due.

How Each Homework Will Be Graded. Your score for each homework assignment will be the sum of your scores of the problems renormalized so that the maximum possible score on each assignment is 10 points.

Homework Assignments

• Assignments on Topics Covered on the First Exam
• Assignments on Topics Covered on the Second Exam
• Assignments on Additional Topics Covered on the Final Exam

Assignments on Topics Covered on the First Exam (Monday, 5 October)

• Friday, 4 September (Real Numbers)
  
  • Fitzpatrick, Section 1.1: 2, 5, 14, 16, 19.
  • Fitzpatrick, Section 1.2: 3, 4, 5.
  • Fitzpatrick, Section 1.3: 3, 4, 12, 17.
• Friday, 11 September (Real Numbers plus Sequences)
  
  • Prove assertion (a) of Proposition 1.17 on page 10 of the notes.
  • Prove assertion (b) of Proposition 1.17 on page 10 of the notes.
  • Prove assertion (a) of Proposition 1.18 on page 10 of the notes.
  • Prove the exercise at the bottom of page 11 of the notes.
  • Fitzpatrick, Section 2.1: 1, 3, 18.
  • Fitzpatrick, Section 2.4: 1, 2, 3.
  • Show that cos(k) > .5 frequently as k tends to infinity.
  • Prove Proposition 2.7 in the notes.
• Wednesday, 24 September (Sequences)
  
  • Fitzpatrick, Section 2.3: 1, 3, 7.
  • Additional Problems (click on date above).
• Monday, 28 September (Series)
  
  • Fitzpatrick, Section 9.1: 1, 2, 3, 4.
  • Additional Problems (click on date above).
• Friday, 2 October (Series plus Sets)
  
  • All Problems (click on date above).
• Wednesday, 7 October (Sets plus practice for first exam)
  
  • All Problems (click on date above).

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Assignments on Topics Covered on the Second Exam (Friday, 6 November)

• Wednesday, 14 October (Functions, Limits, Continuity)
  
  • Fitzpatrick, Section 3.1: 6, 9.
  • Fitzpatrick, Section 3.5: 2, 4.
  • Fitzpatrick, Section 3.2: 1, 5.
  • Fitzpatrick, Section 3.3: 1, 6.
  • Fitzpatrick, Section 3.6: 6.
  • Fitzpatrick, Section 3.7: 2, 9.
  • Additional Problems (click on date above).
• Wednesday, 21 October (Differentiability and Derivatives)
  
  • Fitzpatrick, Section 4.1: 1, 5, 9, 15.
  • Fitzpatrick, Section 4.2: 1, 6, 9.
  • Additional Problems (click on date above).
• Wednesday, 28 October (Mean-Value Theorems and Applications)
  
  • Fitzpatrick, Section 4.3: 1, 7, 11, 12, 16, 20, 21.
  • Fitzpatrick, Section 8.1: 2, 4.
  • Fitzpatrick, Section 8.2: 1, 8, 11.
  • Fitzpatrick, Section 8.3: 1, 2, 4.
  • Additional Problems (click on date above).
• Wednesday, 4 November (Mean-Value Theorems and Applications plus Uniform Continuity)
  
  • Fitzpatrick, Section 4.4: 3, 5, 7.
  • Fitzpatrick, Section 3.4: 1, 3, 5, 6, 7.
  • Additional Problem (click on date above).
• Monday, 9 November (Uniform Continuity plus practice for Second Exam)
  
  • All Problems (click on date above).

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Assignments on Additional Topics Covered on the Final Exam (Friday, 18 December)

• Monday, 16 November (Riemann Integral)
  
  • Fitzpatrick, Section 6.1: 1, 3, 6, 7.
  • Fitzpatrick, Section 6.2: 2, 4.
  • Fitzpatrick, Section 7.3: 6, 10, 11, 12.
  • Additional Problems (click on date above).
• Monday, 23 November (Riemann Integrable Functions)
  
  • Fitzpatrick, Section 6.3: 2.
  • Fitzpatrick, Section 6.4: 1, 3, 6, 9.
  • Additional Problems (click on date above).
• Friday, 4 December (Fundamental Theorems of Calculus)
  
  • Fitzpatrick, Section 6.5: 1, 5.
  • Fitzpatrick, Section 6.6: 1, 3, 7.
  • Fitzpatrick, Section 7.2: 3, 4, 5. 9.
  • Additional Problems (click on date above).
• Friday, 11 December (Sequences and Series of Functions)
  
  • Fitzpatrick, Section 9.2: 1, 4, 6.
  • Fitzpatrick, Section 9.3: 1, 4, 6.
  • Fitzpatrick, Section 9.4: 3, 4.
  • Fitzpatrick, Section 9.5: 1, 4, 7, 10.
  • Additional Problems (click on date above).
• Friday, 18 December (Practice for Final Exam)
  (Not Collected)
  

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